Temperature definition

I am in high school chemistry, and we are learning about gases. We were told that temperature is a measurement of the average kinetic energy of the particles. We were told that the reason water evaporates is because some of the particles in the water have high kinetic energy (higher than the boiling point) and escape and become gases. I was wondering if there is ever particles in the water that have very low kinetic energy and solidify, just like some particles evaporate.

1) Consider liquid water in contact with a gaseous mixture of air and water
vapour. Water evaporates when the vapour pressure of the liquid water
is greater than the partial pressure of water vapour in the gas; i.e.
when the rate at which molecules leaving the liquid is greater than the
rate at which they are entering the liquid from the gas. Water will
evaporate only until there is a state of (dynamic) equilibrium between
the liquid and the vapour.
2) In general, molecules of water near the liquid-gas boundary may escape
from the liquid provided they have a small energy necessary to overcome
any surface forces. Molecules with a whole range of kinetic energy can
leave the liquid, not just those with extremely high energies.
(Incidentally, what do you mean by kinetic energy higher than the boiling
point?)
3) Freezing is a collective event. A single molecule cannot "freeze". At any
given instant, there may be many molecules with small or even zero
kinetic energy but these will be jostled by their more energetic
neighbours within a very short time, so there is no local freezing
possible at temperatures above the freezing point.

Staff: Mentor

Just a little more - pkleinod's explanation tells us why water can exist as a gas and a liquid together in stable equilibrium at, say, 10C, but not water and ice. But at 0C, it is possible for all three to exist in a stable equilibrium with each other and ice will form and melt in a stable equilibrium much the same way water will condense and evaporate in a stable equilibrium.

Thank you russ_watters. Yes, at the triple point, ice, liquid water and water vapour can coexist at equilibrium. Just a small correction: the triple point of water does not occur at 0 o C (=273.15 K). The temperatures and pressures are the following:
For ice I, water(l), water(g): T = 0.0099o C (273.16 K);
P = 0.00603 atm (611 Pa; 4.58 mm Hg)
1 atm = 101 325 Pa.
This is a small point in the context of the original post.